The answer is: " 355 " .
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The length of the longest side of ΔQRS is: " 355 " .
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Explanation:
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Given:
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The smallest side of ΔQRS is 280.
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In ΔEFG, the smallest side is 112 {compared to "144" and "128"}.
The longest side length of ΔEFG is "144" {compared to "128" and "112"}.
What is the length of the largest side of ΔQRS ?
Both triangles are similar, so the following ratios can be set up to solve the problem:
(the smallest side length of ΔEFG) / (the smallest side length of ΔQRS) =
(the longest side length of ΔEFG) / (the longest side length of ΔQRS) ;
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→ 112/ 280 = 144 / (the longest side length of ΔQRS);
We wish to solve for "(the longest side length of ΔQRS)" ;'
for which we shall represent with the variable, "x" ;
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→ Rewrite as: 112/280 = 144/ x ;
Reduce "112/180" to: "2/5" ;
and rewrite: "2/5 = 144/x " ;
Cross multiply: 2x = 5(144) ;
Divide EACH SIDE of the equation by "2" ; to isolate "x" on one side of the equation; & to solve for "x" :
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2x/ 2 = [tex] \frac{5(144)}{2} [/tex] ;
x = 5 * [tex] \frac{144}{2}[/tex] ;
x = 5 * 71 ;
x = 355 .
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The answer is: "355" .
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The length of the longest side of ΔQRS is: "355" .
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