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# The perimeter of an isosceles triangle is 14 cm and the ratio of the lateral side to the base is 5:4. Find the area of the triangle

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## The perimeter of an isosceles triangle is 14 cm and the ratio of the lateral side to the base is 5:4. Find the area of the triangle

Guest Jun 11, 2015

#1
+85581
+10

Assuming that the lateral sides are the equal ones, we have

x + 2*(5/4)x  = 14

x + (10/4)x  = 14

(14/4)x  = 14     multiply both sides by 4

14x  = 56         divide both sides by 14

x = 4 cm      and this is the base......and (5/4)x = (5/4)(4) = 5 cm......and this is a lateral side

And by the Pythagorean Theorem, the height will be √[5^2 - 2^2] = √21 cm

So....the area of the triangle will be    (1/2)bh  =  (1/2)(4)√21   =  2√21 cm  ≈ 9.165 cm^2

CPhill  Jun 11, 2015
Sort:

#1
+85581
+10

Assuming that the lateral sides are the equal ones, we have

x + 2*(5/4)x  = 14

x + (10/4)x  = 14

(14/4)x  = 14     multiply both sides by 4

14x  = 56         divide both sides by 14

x = 4 cm      and this is the base......and (5/4)x = (5/4)(4) = 5 cm......and this is a lateral side

And by the Pythagorean Theorem, the height will be √[5^2 - 2^2] = √21 cm

So....the area of the triangle will be    (1/2)bh  =  (1/2)(4)√21   =  2√21 cm  ≈ 9.165 cm^2

CPhill  Jun 11, 2015

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