Question

The line segment the joining the mid-points of two consecutive sides of a rectangle is 15 cm. The length of a diagonal of the rectangle is ​

Answer 1

Answer:

30 cm

Step-by-step explanation:

By using theorem,

In a triangle, line segment joining the midpoints of two sides is parallel to third side and equals to half of it in magnitude.

Answer 2

Answer:

The length of the diagonal of the rectangle is 30 cm.

Step-by-step explanation:

Let's consider a rectangle ABCD and let E and F be the midpoints of AB and BC, respectively. Let's also denote the length of AB by a and the length of BC by b.

Since E and F are midpoints of their respective sides, we have:

AE = EB = a/2

BF = FC = b/2

We can draw the diagonal AC of the rectangle, which divides it into two congruent right triangles, ACD and ABC.

Using the Pythagorean theorem, we can express the length of AC in terms of a and b:

AC² = AD² + DC²

AC² = a² + b² (since AD = BC = b, and DC = AB = a)

Now, let's consider the right triangle AEF. We know that EF = 15 cm, and we can use the Pythagorean theorem to relate EF to the sides of the rectangle:

EF² = AE² + AF²

EF² = (a/2)² + (b/2)²

EF² = (a² + b²)/4

We can simplify this equation by substituting AC² = a² + b²:

EF² = AC²/4

Taking the square root of both sides, we get:

EF = AC/2

So, we have:

AC = 2EF = 2(15 cm) = 30 cm

Now that we know the length of AC, we can use the Pythagorean theorem again to find the length of the diagonal BD:

BD² = AB² + AD²

BD² = a² + b²

Since AC and BD are diagonals of a rectangle, they are congruent, so we have:

AC = BD = 30 cm

Therefore, the length of the diagonal of the rectangle is 30 cm.

To learn more about rectangle: brainly.in/question/19886109

To learn more about diagonal: brainly.in/question/37590271

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