Question

BERE 6 1011 THE DIAGRAM SHOWS THREE SQUARES WHOSE SIDE LENGTHS MEET TO FORM A RIGHT TRIANGLE. USE THE DIAGRAM TO TYPE THE SOLUTION TO EACH QUESTION BELOW. If the area of square 1 A is 225 ft2 and the area of square B is 400 ft2, what is the area of If the area of square 2 A is 81 ft2 and the area of square C is 1,681 ft2, what is the area of C square C? square B? А If the perimeter of A 3 is 36 ft and the perimeter of B is 48 ft, what is the perimeter of If the area of C is 400 ft2 and the perimeter of B is 64 ft, what is the side length of square A? B square C? Messwering the Medla IC. 2019 C 1

Answer 1

The area of a square is L X L

A = l x l

Where l is the side of the square

`\begin{gathered} \text{Square A = 225ft}^2 \\ \text{Square B = 400ft}^2 \\ \text{Square A and square B form a right angle triangle to one side of the square C} \\ \text{ Since, Area of a square = l}^2 \\ \text{For Square A } \\ 225=l^2 \\ \text{Take the squareroot of both sides} \\ l\text{ = }\sqrt[]{225} \\ l\text{ = 15ft} \\ \text{For square B} \\ 400=l^2 \\ \text{Take the square root of both sides} \\ l\text{ = }\sqrt[]{400} \\ l\text{ = 20 ft} \\ To\text{ find one side of square C, we n}eed\text{ to apply Pythagora's theorem} \\ \text{Hypotenus}^2=opposite^2+adjacent^2 \\ \text{Opposite = 15, and adjacent = 20} \\ \text{Hypotenus}^2=15^2+20^2 \\ \text{Hypotenus}^2\text{ = 225 + 400} \\ \text{Hypotenus}^2\text{ = 625} \\ \text{Take the square root of both sides} \\ \text{hypotenus = }\sqrt[]{625} \\ \text{Hypotenus = 25ft} \\ \text{Hence, the area of Square C} \\ \text{Square C = 25 x 25} \\ \text{Square C = 625ft}^2 \end{gathered}`

Question 2

Area of Square C = Area of Square A + Area of square B

`\begin{gathered} \text{Area of square C = 1681 ft}^2 \\ \text{Area of square A = 81 ft}^2 \\ \text{Area of Square C = Area of square B + Area of Square A} \\ \text{Area of Square B = Area of square C - Area of Square A} \\ \text{Area of square B = 1681 - 81} \\ \text{Area of square B = 1600 ft}^2 \end{gathered}`