Question

NEED ANSWER!! WILL GIVE BRAINLIEST TO FIRST CORRECT

Points A, B, C, D, and E lie on the given circle. Point I is the common vertex of four squares shown on the picture. Area of square ABIG is 144 square units. Area of square MEIH is 100 square units. Find area of square DKIL.

please provide a step-by-step explanation!!!

Answer 1

Area of the square DKIL = 25 square units

Solution:

In the given image A, B, C, D and E lie on the circle.

Point I is the common vertex of four squares.

Area of ABIG = 144 square units

Area of MEIH = 100 square units

We know that area of square = side × side

Area of MEIH = 100  square units

Side IE × Side IE = 100

$(IE)^{2}=100$

Taking square root on both sides

IE = 10 units

$I L=\frac{1}{2} \times I E$

$I L=\frac{1}{2} \times 10$

IL = 5 units

In a square all sides are equal.

Therefore, IL = LD = DK = IK = 5 units

area of square = side × side

area of square DKIL = IL × IL

                                   = 5 × 5

area of square DKIL = 25 square units

Hence, area of the square DKIL is 25 square units.