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3 years ago

1. Construct the Isosceles triangle from given data below : Altitude = 55mm Perimeter = 135mm

Mathematics

1 answer:

GuDViN [60]3 years ago

5 0

Answer:

base: 22 37/54; sides: 56 17/108

Step-by-step explanation:

If we let x represent half the length of the base, and y represent the length of the side, then we have ...

2x +2y = 135 . . . . . perimeter relation

x^2 +55^2 = y^2 . . . . Pythagorean theorem relation

Solving for y and substituting into the second equation, we have ...

y = 135/2 -x

x^2 + 3025 = (67.5 -x)^2

3025 = -135x +4556.25 . . . . . . expand, subtract x^2

135x = 1531.25 . . . . . . . . . . add 135x -3025

x = 1531.25/135 = 11 37/108

The length of the base is double this value, 22 37/54.

The length of each side is 67.5 -11 37/108 = 56 17/108.

<em>Check</em>

The perimeter is the base plus two side lengths:

22 37/54 + 2(56 17/108) = (22 +112) +37/54 +17/54 = 134 +1 = 135.

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