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Reika [66]
3 years ago
12

The perimeter of an isosceles trapezoid is 28 in and the ratio of lengths of its bases is 5:3. Find the lengths of the sides of

the trapezoid if its diagonal bisects the angle at the longer base. Answer:
Mathematics
1 answer:
wariber [46]3 years ago
5 0
The measurements are:<span>
b</span>₁ = 8.4 inches; b₂ = 14 inches; leg₁ = 2.8 inches; leg₂ = 2.8 inches<span>

Let x = length of base and leg

The formula for perimeter of isosceles trapezoid is P = b₁ + b₂ + 2(leg)</span><span>
Where: b = base

<span>       P = b</span>₁ + b₂ + 2(leg)</span><span>
<span>     28 = 3x + 5x + 2(x)</span>
<span>     28 = 8x + 2x</span>
28/10 = 10x/10
<span>    2.8 = x</span>

Now, substitute the values:
<span>       P = b</span>₁ + b₂ + 2(leg)</span><span>
<span>     28 = 3(2.8) + 5(2.8) + 2(2.8)</span>
     28 = 8.4 + 14 + 5.6
     28 = 28

Hence the measurements are:
b₁ = 8.4 inches; b₂ = 14 inches; leg₁ = 2.8 inches; leg₂<span> = 2.8 inches</span></span>
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