Shown below is a rectangle and an isosceles right triangle.777101010What is the area of the rectangle?

Name: Video Solution: Calculate Rectangle Area: 7-Unit Triangle and 10-Unit Height Problem
Description: Step-by-step video solution

Calculate Rectangle Area: 7-Unit Triangle and 10-Unit Height Problem

Shown below is a rectangle and an isosceles right triangle.

What is the area of the rectangle?

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Step-by-step video solution

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00:00 Determine the area of the rectangle

00:06 Apply the Pythagorean theorem to the triangle ABC

00:12 The triangle is isosceles according to the given data

00:17 Substitute in the relevant values and solve to find AC

00:24 Extract the root

00:28 This is the length of side AC

00:35 Apply the formula for calculating the area of a rectangle

00:41 Side(AC) X by side(AE)

00:44 Substitute in the relevant values and proceed to solve

00:47 This is the solution

Step-by-step written solution

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Understand the problem

Shown below is a rectangle and an isosceles right triangle.

What is the area of the rectangle?

Step-by-step solution

To find the missing side, we use the Pythagorean theorem in the upper triangle.

Since the triangle is isosceles, we know that the length of both sides is 7.

Therefore, we apply Pythagoras $A^2+B^2=C^2$ $7^2+7^2=49+49=98$

Therefore, the area of the missing side is: $\sqrt{98}$

The area of a rectangle is the multiplication of the sides, therefore:

$\sqrt{98}\times10=98.99\approx99$

Final Answer

$\approx99$

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Calculate Rectangle Area: 7-Unit Triangle and 10-Unit Height Problem

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Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Practice Quiz

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