If the larger base of an isosceles trapezoid equals a diagonal and the smaller base equals the altitude, then the ratio of the smaller base to the larger base is :

1/2

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2/3

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3/4

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3/5

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2/5

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Solution

The correct option is C 3/5
$⟹ b^{2} + {(\frac{b + c}{2})}^{2} = c^{2} ⟹ 4 b^{2} + b^{2} + c^{2} + 2 b c = 4 c^{2} ⟹ 5 b^{2} + 2 b c - 3 c^{2} = 0 ⟹ 5 b (b + c) - 3 c (b + c) = 0 ∴ 5 b = 3 c ⟹ \frac{b}{c} = \frac{3}{5} (b \neq c)$
Ratio of smaller base to larger base = $\frac{3}{5}$

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If the larger base of an isosceles trapezoid equals a diagonal and the smaller base equals the altitude, then the ratio of the smaller base to the larger base is :

The correct option is C 3/5⟹b2+(b+c2)2=c2⟹4b2+b2+c2+2bc=4c2⟹5b2+2bc−3c2=0⟹5b(b+c)−3c(b+c)=0∴5b=3c⟹bc=35(b≠c)Ratio of smaller base to larger base = 35

The correct option is C 3/5
$⟹ b^{2} + {(\frac{b + c}{2})}^{2} = c^{2} ⟹ 4 b^{2} + b^{2} + c^{2} + 2 b c = 4 c^{2} ⟹ 5 b^{2} + 2 b c - 3 c^{2} = 0 ⟹ 5 b (b + c) - 3 c (b + c) = 0 ∴ 5 b = 3 c ⟹ \frac{b}{c} = \frac{3}{5} (b \neq c)$
Ratio of smaller base to larger base = $\frac{3}{5}$