Question

1. each right triangle has an unknown side length. suppose a square is drawn along the unknown side. which square will have an area of 24 cm²? a (triangle with legs 3 cm and 4 cm) b (triangle with leg 9 cm and hypotenuse 10 cm) c (triangle with legs 3.1 cm and 4.2 cm) d (triangle with legs 5 cm and 7 cm) 8. which statement is true for this triangle? (right triangle with legs a, b and hypotenuse h) a ( b^2 + h^2 = a^2 ) b ( b^2 + a^2 = h^2 ) c ( h^2 + a^2 = b^2 ) d none of the above

Explanation:

Question 7

Step1: Recall Pythagorean theorem

For a right triangle, \( c^2 = a^2 + b^2 \) (where \( c \) is hypotenuse, \( a,b \) are legs). The area of the square on the unknown side is \( c^2 \) (if hypotenuse) or \( |a^2 - b^2| \) (if leg).

Step2: Analyze Option A

Legs: \( 3 \, \text{cm}, 4 \, \text{cm} \). Hypotenuse squared: \( 3^2 + 4^2 = 9 + 16 = 25 \). Area of square: \( 25 \, \text{cm}^2
eq 24 \).

Step3: Analyze Option B

Leg: \( 9 \, \text{cm} \), Hypotenuse: \( 10 \, \text{cm} \). Unknown leg squared: \( 10^2 - 9^2 = 100 - 81 = 19 \). Area: \( 19 \, \text{cm}^2
eq 24 \).

Step4: Analyze Option C

Legs: \( 3.1 \, \text{cm}, 4.2 \, \text{cm} \). Hypotenuse squared: \( 3.1^2 + 4.2^2 = 9.61 + 17.64 = 27.25 \). Area: \( 27.25 \, \text{cm}^2
eq 24 \).

Step5: Analyze Option D

Leg: \( 5 \, \text{cm} \), Hypotenuse: \( 7 \, \text{cm} \). Unknown leg squared: \( 7^2 - 5^2 = 49 - 25 = 24 \). Area of square: \( 24 \, \text{cm}^2 \).

Step1: Recall Pythagorean theorem

In a right triangle, \( (\text{leg}_1)^2 + (\text{leg}_2)^2 = (\text{hypotenuse})^2 \). Here, legs are \( a, b \), hypotenuse is \( h \).

Step2: Apply theorem

So \( a^2 + b^2 = h^2 \).

Answer:

D

Question 8