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kaheart [24]
3 years ago
6

The perimeter of a rectangle is 60 meters.if the length of the rectangle is 14 meters.what is the width of the rectangle?

Mathematics
1 answer:
alexandr1967 [171]3 years ago
4 0
P=2l+2w
60=14*2+2w
60=28+2w
 -28      -28
32=2w
/2  /2
16=w
The width of the rectangle is 16 m

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Molodets [167]

m∠1 = 30° (by Vertical angle theorem)

m∠A = 80° (by Triangle sum theorem)

m∠D = 80° (by Triangle sum theorem)

The value of x is 7.5 and y is 9.

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∠ACB and ∠DCE are vertically opposite angles.

Vertical angle theorem:

<em>If two lines are intersecting, then vertically opposite angles are congruent.</em>

⇒ m∠DCE = m∠ACB

⇒ m∠1 = 30° (by Vertical angle theorem)

In triangle ACD,

Triangle sum property:

<em>Sum of the interior angles of the triangle = 180°</em>

⇒ m∠A + m∠C + m∠B = 180°

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⇒ m∠A = 80° (by Triangle sum theorem)

Similarly, m∠D = 80° (by Triangle sum theorem)

In ΔACD and ΔDCE,

All the angles are congruent, so ΔACD and ΔDCE are similar triangles.

<em>In similar triangle corresponding sides are in the same ratio.</em>

$\frac{9}{12}=\frac{x}{10}

Do cross multiplication.

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7.5 = x

Now, to find y:

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Divide by 9, we get

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Hence the value of x is 7.5 and y is 9.

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