Question

Find the missing side of a right triangle if

a. area = 46cm 2 , base = 23cm
b. area = 120cm 2 , base = 40cm
c. area =12m 2 , base = 20m

Grade#8

Answer 1

Answer:

a. h = 8cm
b. h = 12cm
c. h = 2.4m

Step by step explanation :

To find the missing side of a right triangle, we need to use the formula for the area of a triangle, which is:

Area = (1/2) x base x height

where base is one of the sides of the triangle, and height is the length of the perpendicular drawn to that base.

a. Given that the area of the triangle is 46cm² and the base is 23cm, we can find the height as follows:

46cm² = (1/2) x 23cm x height

Simplifying the equation, we get:

height = (2 x 46cm²) / 23cm

height = 4cm x 2 = 8cm

Therefore, the missing side of the right triangle is 8cm.

b. Given that the area of the triangle is 120cm² and the base is 40cm, we can find the height as follows:

120cm² = (1/2) x 40cm x height

Simplifying the equation, we get:

height = (2 x 120cm²) / 40cm

height = 6cm x 2 = 12cm

Therefore, the missing side of the right triangle is 12cm.

c. Given that the area of the triangle is 12m² and the base is 20m, we can find the height as follows:

12m² = (1/2) x 20m x height

Simplifying the equation, we get:

height = (2 x 12m²) / 20m

height = 1.2m x 2 = 2.4m

Therefore, the missing side of the right triangle is 2.4m.

Answer 2

a. The area of a triangle is given by the formula A = (1/2)bh, where b is the base and h is the height. We know that A = 46cm^2 and b = 23cm. Substituting these values into the formula, we get:

46cm^2 = (1/2)(23cm)(h)

Simplifying, we get:

46cm^2 = 11.5cm*h

Dividing both sides by 11.5cm, we get:

h = 4cm

Therefore, the missing side of the right triangle is 4cm.

b. Using the same formula, we can find the height of the triangle:

120cm^2 = (1/2)(40cm)(h)

Simplifying, we get:

120cm^2 = 20cm*h

Dividing both sides by 20cm, we get:

h = 6cm

Therefore, the missing side of the right triangle is 6cm.

c. Again, using the same formula, we can find the height of the triangle:

12m^2 = (1/2)(20m)(h)

Simplifying, we get:

12m^2 = 10m*h

Dividing both sides by 10m, we get:

h = 1.2m

Therefore, the missing side of the right triangle is 1.2m.