Question

In a rectangle, one side is 7 cm longer than the other and the diagonal is 13 cm. Calculate the area of the rectangle

198

likes

992 views

Answer to a math question In a rectangle, one side is 7 cm longer than the other and the diagonal is 13 cm. Calculate the area of the rectangle

$Expert avatar$

Fred

4.4

113 Answers

Let one side of the rectangle be x cm, then the other side will be (x+7) cm.

We know that the diagonal of a rectangle forms a right triangle with the sides of the rectangle. So, we can use the Pythagorean theorem to find the relationship between the sides of the rectangle:

x^2 + (x+7)^2 = 13^2

Expanding and simplifying:

x^2 + x^2 + 14x + 49 = 169

2x^2 + 14x - 120 = 0

Dividing the equation by 2 to simplify:

x^2 + 7x - 60 = 0

Factoring the quadratic equation:

(x+12)(x-5) = 0

So, x = 5 cm (as the side length of a rectangle can't be negative).

Therefore, the sides of the rectangle are 5 cm and 12 cm.

The area of a rectangle is given by the formula:

Area = length \times width

Therefore, the area of the rectangle is:

Area = 5 \times 12 = 60 \, cm^2

\boxed{60 \, cm^2}

is the area of the rectangle.

Frequently asked questions (FAQs)

What is the value of sin(45°) + cos(45°) - tan(45°) + csc(45°) - sec(45°)?

What is the distance from the origin to the point (-3, 4) in a circle with radius 5?

Question: What are the component values of a unit vector pointing in the direction of a line with equation y = 2x + 1?

New questions in Mathematics

calculate the derivative by the limit definition: f(x) = 6x^3 + 2

CASE 6-1: PREPARE A PRODUCTION PLAN: WHAT PROBLEMS ARRIVE? Midwest Plastics Company has conducted profit planning for several years. The president stated (with justification) that inventory control and planning had not been satisfactory, which was mainly due to poor planning of production and inventory budgets. Please analyze and provide recommendations, in detail, on the issue regarding the 20B profit plan, which is now being prepared. Their analysis and recommendations will be presented to the executive committee. Despite the seasonality factor, the sales department has been successful in developing a sales plan, on a monthly basis, for each year. The following sales data is available for 20B. 1. Sales plan summary for 20B: 2. Finished goods inventory, as of January 1, 20B, is 96,000 units. 3. Work-in-process inventory will remain constant. 4. Actual annual sales in 20A, including the estimate for December, were 350,000 units. 5. The average finished goods inventory during 20A was 70,000 units. IT IS REQUESTED. 1. Prepare the annual production budget, assuming that management policy is to budget ending finished goods inventory at a standard quantity, based on the ratio of historical sales of 20A to inventory turnover. 2. Prepare a schedule showing sales, production, and inventory levels for each month, assuming: 1) stable inventory, 2) stable production, and 3) recommended inventory-production levels. In developing your recommendations, assume that the following policies have been established: a) The president has set the policy that a maximum inventory of 85,000 units and a minimum inventory of 75,000 units should be used, except in abnormal circumstances. b) A stable level of production is definitely preferred, except that during the holiday season in July and August, production may be reduced by 25 percent. Likewise, a variation in production of 7.5 percent above and below the average level is acceptable. 3. What are the main problems faced by the company in production planning? Make your general recommendations.