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Papessa [141]
3 years ago
11

find the length of the long diagonal of a rhombus when it's area of 24 square centimeters and it's short diagonal is 4 centimete

rs​

Mathematics
1 answer:
Ivahew [28]3 years ago
6 0

Answer:

12

Step-by-step explanation:

A rhombus is a parallelogram with all four sides equal.

Its diagonals are perpendicular.

Each of the triangles formed by the diagonals and the sides are congruent, so the area of the rhombus is 4 times the area of one of the triangles.

Since the short diagonal is given as 4, each of the triangles can be viewed as having a base of 2.  Each triangle's height, h, then is one half the length of the long diagonal.

The are of one of the triangles is 1/2 (base)(height)=(1/2)(2)h

The area of the rhombus is then

4(1/2)(2)h=24

Solving for h gives

h=6

This makes the length of the long diagonal 2h=12

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Read 2 more answers
Does anyone know the answer?
motikmotik

Answer:

We conclude that the area of the right triangle is:

A\:=p^2-2p-3

Hence, option A is correct.          

Step-by-step explanation:

From the given right-angled triangle,

  • Base = p+1
  • Perpendicular = 2p-6

Using the formula to determine the area of the right-angled triangle

Area of the right triangle A = 1/2 × Base × Perpendicular

                                            =\frac{1}{2}\left(p+1\right)\left(2p-6\right)

Factor 2p-6: 2(p-3)

                                             =\frac{\left(p+1\right)\times \:2\left(p-3\right)}{2}  

Divide the number: 2/2 = 1

                                              =\left(p+1\right)\left(p-3\right)

\mathrm{Apply\:FOIL\:method}:\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd

                                               =pp+p\left(-3\right)+1\cdot \:p+1\cdot \left(-3\right)

                                               =pp-3p+1\cdot \:p-1\cdot \:3

                                                =p^2-2p-3

Therefore, we conclude that the area of the right triangle is:

A\:=p^2-2p-3

Hence, option A is correct.                                        

3 0
3 years ago
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