If the area of a triangle whose base is 22 cm is equ equal to the area of a circle of radius 7 cm, Find the height of the triangle.
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Answer:
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Step-by-step explanation:
First, find the area of the given circle. The formula for the area of a circle is A =r² (We'll use the rational approximation for of 22/7)
Substituting into the formula for = 22/7 and r = 7 cm, we have:
A = (22/7)(7 cm)²
= (22/7)(7²) cm²
= (22/7)(49) cm²
= (22/7)(49/1) cm²
Cancelling the 7 into the 49, we get:
= (22/1)(7/1) cm²
= (154/1) cm²
A = 154 cm² is the area of the circle
Now, the area of a triangle is A = (1/2)bh, where b is the length of the base of the triangle and h is the height of the triangle.
Since we know that the length of the base of the given triangle is b = 22 cm and that the area of the given triangle is equal to the area of the given circle, then we can substitute into the formula for the area of a triangle to find the height h of the given triangle as follows:
A = (1/2)bh
154 cm² = (1/2)(22 cm)h
154 cm² = (11 cm)h
Now, dividing both sides of the equation by 11 cm to find height h, we have:
(154 cm²)/(11 cm) = [(11 cm)/(11 cm)]h
14 cm = (1)h
h = 14 cm is the height of the given triangle.