Question

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?

Answer 1

Area of the rectangle `=7*sqrt161=88.82" "`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=sqrt161`

Compute now for the area of the rectangle

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

Area `=b*x`

Area `=7*sqrt161`

Area `=88.82`

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

Answer 2

`88.8` `units`

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

`rarr8^2+b^2=15^2`

`rarr64+b^2=225`

`rarrb^2=225-64`

`rarrb^2=161`

`rArrb=sqrt161`

Now we need to find the area of the rectangle

Area of rectangle

`color(blue)(l*b` `units`

`l=l` `e` `ng` `t` `h,b=breadth`

Where

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

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