# QOTD-Geometry-Find the length of side SB

2019-07-03 | Team PendulumEdu

A rectangular plane is cut into four triangles in such a way that the area of triangle APQ, ASB and BRQ is equal. Length of side BR is 4 cm. Find the length of SB. A.  $$(1+2\sqrt{5})m$$

B. $$(\sqrt{5}-2)m$$

C. $$2(\sqrt{5}-1)m$$

D. $$2(1+\sqrt{5})m$$

Solution

Let the length of side SB = x

Length of side AS = y

Length of side PA = z

So, now $$PQ = x + 4$$ and$$QR = y + z$$ According to the question

Area of triangle APQ = Area of triangle ASB = Area of triangle BRQ

$$\frac{1}{2}* z* (x+4)= \frac{1}{2} * y* x = \frac{1}{2}* (y+z)* 4$$

$$z*(x+4)= y+z* 4$$……………………………..(1)

$$z*x+4= y*x$$ ……………………………………….(2)

Using equation (1), we get

$$4y+4z=zx+4z$$

$$Z=\frac{4y}{x}$$

Now, substituting the value of z in equation (2), we get

$$\frac{4y}{x}*(x+4)=x*y$$

$$x^{2} - 4x - 16=0$$

$$x=2(1\pm\sqrt{5})$$

Length cannot be negative, therefore  $$SB=2(1+\sqrt{5})$$

Hence, (d) is the correct option.

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