The surface area of the wooden door is $416$ $m^{2}$ . The length and width of the door is $12$ m and $10$ m respectively. Find its height.

2 m

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4 m

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6 m

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8 m

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Solution

The correct option is A $4 m$
Surface area $= 2 ($ Length $\times$ width $+$ Length $\times$ height $+$ Width $\times$ height $)$
Length $= 12$ m; Height $= ?$ m; Width $= 10$ m
Assume height $= x$
$\Rightarrow 416 = 2 \times (12 \times 10 + 12 \times x + 10 \times x)$
$\Rightarrow 416 = 2 \times (120 + 12 x + 10 x)$
$\Rightarrow 416 = 2 \times (120 + 22 x)$
$\Rightarrow \frac{416}{2} = 120 + 22 x$
$\Rightarrow 208 - 120 = 22 x$
$\Rightarrow 88 = 22 x$
$\Rightarrow x = 4$ m

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The surface area of the wooden door is 416 m2. The length and width of the door is 12 m and 10 m respectively. Find its height.

The correct option is A 4mSurface area =2(Length × width + Length × height + Width × height)Length =12 m; Height =? m; Width =10 mAssume height =x⇒416=2×(12×10+12×x+10×x)⇒416=2×(120+12x+10x)⇒416=2×(120+22x)⇒4162=120+22x⇒208−120=22x⇒88=22x⇒x=4 m

The surface area of the wooden door is $416$ $m^{2}$ . The length and width of the door is $12$ m and $10$ m respectively. Find its height.