# A right triangle has sides A, B, and C. Side A is the hypotenuse and side B is also a side of a rectangle. Sides A, C, and the side of the rectangle adjacent to side B have lengths of 15 , 8 , and 7 , respectively. What is the rectangle's area?

Area of the rectangle $= 7 \cdot \sqrt{161} = 88.82 \text{ }$square units

#### Explanation:

We can compute for side $b$
because by Pythagorean Theorem

${a}^{2} = {b}^{2} + {c}^{2}$

${15}^{2} = {b}^{2} + {8}^{2}$

${b}^{2} = 225 - 64$

$b = \sqrt{161}$

Compute now for the area of the rectangle

Let $x = 7$ be the length of the other side of the rectangle

Area $= b \cdot x$

Area $= 7 \cdot \sqrt{161}$

Area $= 88.82$

God bless....I hope the explanation is useful.

Mar 25, 2016

$88.8$ $u n i t s$

#### Explanation:

Consider the diagram

Use the Pythagorean theorem to find the length of $b$

color(blue)(a^2+b^2=c^2

Where

color(red)(a=c,b=b,c=a

A little confusion! yeah

Remember like this

The square of Hypotenuse of a right triangle equals the sum of the squares of the other two sides

$\rightarrow {8}^{2} + {b}^{2} = {15}^{2}$

$\rightarrow 64 + {b}^{2} = 225$

$\rightarrow {b}^{2} = 225 - 64$

$\rightarrow {b}^{2} = 161$

$\Rightarrow b = \sqrt{161}$

Now we need to find the area of the rectangle

Area of rectangle

color(blue)(l*b $u n i t s$

$l = l$$e$$n g$$t$$h , b = b r e a \mathrm{dt} h$

Where

color(red)(l=sqrt161,b=7

:.color(green)(Area=7sqrt161~~88.89