If one diagonal of a rhombus is 15 meters long and it’s area is 157.5 square meters, find the measures of the other diagonal

The other diagonal measures 21m

Step-by-step explanation:

In this question, we are tasked with calculating the length of the second diagonal of as Rhombus given the measure of the surface area of the rhombus and the length of the other diagonal

Mathematically, for a rhombus having two diagonals and , the area of the rhombus can be calculated mathematically using the formula below;

A = 1/2 × ×

From the question, we can identify that A = 157.5 and = 15m

we input these in the formula;

157.5 = 1/2 × 15 ×

315 = 15

= 315/15

= 21m

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺