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Fiesta28 [93]
3 years ago
6

Please solve

Mathematics
1 answer:
lisov135 [29]3 years ago
7 0

Let lebgth be x

  • Breadth=3x/4

\\ \rm\Rrightarrow Perimeter=2(L+B)

\\ \rm\Rrightarrow 2(x+\dfrac{3x}{4})=140

\\ \rm\Rrightarrow 2\left(\dfrac{4x+3x}{4}\right)=140

\\ \rm\Rrightarrow 2\left(\dfrac{7x}{4}\right)=140

\\ \rm\Rrightarrow \dfrac{14x}{4}=140

\\ \rm\Rrightarrow 14x=140(4)

\\ \rm\Rrightarrow 14x=560

\\ \rm\Rrightarrow x=\dfrac{560}{14}

\\ \rm\Rrightarrow x=40

  • Length=40cm
  • Breadth=3(40)/4=120/4=30[
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In triangle KLM, if K is congruent to L, KL = 9x - 40, LM = 7x - 37, & KM = 3x + 23, find x & the measure of each angle.
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Answer: x = 15, ∠K = 45.7°, ∠L = 45.7°, ∠M = 88.6°

<u>Step-by-step explanation:</u>

Since ∠K ≅ ∠L, then ΔKLM is an isoceles triangle with base KL

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3x + 23 = 7x - 37

       23 = 4x - 37

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Next, draw a perpendicular bisector KN from K to KL. Thus, N is the midpoint of KL and ΔMNL is a right triangle.

  • Since N is the midpoint of KL and KL = 95, then NL = 47.5
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cos ∠L = \frac{47.5}{68}

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      ∠L = 45.7  

Triangle sum Theorem:

∠K + ∠L + ∠M = 180°    

45.7 + 45.7 + ∠M = 180

       91.4     + ∠M = 180

                      ∠M = 88.6

       

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