the length of equal sides of an isosceles triangle is 10 cm and height is 8 cm. Find the height of the triangle and area.
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Answers
Step-by-step explanation:
Given: Isosceles Triangle (ie - 2 sides equal)
Sides are: 3 cm and 7 cm
Find: 3rd side
Plan: Use the Triangle Inequality Theorem
There are 2 choices for the 3rd side of the triangle.
Choice 1: the 3rd side is 3 cm.
The Triangle Inequality states that the sum of any pair of a triangle’s sides is greater then the 3rd side.
Sides are: 3 cm, 3 cm, 7 cm In pairs:
Sum (7, 3) = 10 > 3 ok
Sum (7, 3) = 10 > 3 ok ( It’s an isosceles triangle so this happens twice.)
Sum (3, 3) = 6 not > 7 Fails
The sides cannot be 3 cm, 3 cm, 7 cm
Choice 2: the 3rd side is 7 cm
Sides are: 3 cm, 7 cm, 7 cm In pairs:
Sum (3, 7) = 10 > 7 ok
Sum (3, 7) = 10 > 7 ok ( occurs twice because it’s an isosceles triangle)
Sum (7, 7) = 14 > 3 ok
The Triangle Inequality Theorem is satisfied.
Thus, the 3rd side of the Isosceles Triangle is 7 cm. Q.E.D.
Double Check: ✅ ✅
Answer: 3rd side = 7 cm
Note:
“Q.E.D. or QED is an initialism of the Latin phrase "quod erat demonstrandum", literally meaning "what was to be shown".
Answer:
The equal sides of an isosceles triangle = 8 cm.
The third side = 10 cm.
The altitude of the triangle on the third side as the base
= [8^2–5^2]^0.5 = [64–25]^0.5 = 39^0.5 or 6.244997998 cm.
The area of the triangle = 10*6.244997998/2 = 31.22498999 sq cm
The altitude on the equal sides = 31.22498999*2/8 = 7.806247498 cm.