Question

I have to find the value of z please solve this question
and I will mark you as the brainliest
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Answer 1

Analysis:-

‎ ‎ ‎ ‎ ‎ ‎We're given with a diagram of a trapezium along with its measures of each of its angles. All the values of the trapezium are given as a expressions and variable. Then, what are we asked to find? We're asked to specify the value of the variable in the expressions.

Given data:-

‎ ‎ ‎ ‎ ‎ ‎The measures given as the angles of the trapezium are z°, (z + 7)°, (2z + 39)° and (3z + 6)°

Theory:-

‎ ‎ ‎ ‎ ‎ ‎Here we will be getting to know about the steps of solving the question. First of let's recall the properties of a trapezium!

• A trapezium is a four-sided polygonal figure, i.e, it's a quadrilateral.
• A trapezium has a pair of parallel sides and a pair of non-parallel sides.
• As it has four sides, there will be four vertices where we can find four angles. All these four angles sum up to 360° (which is known as angle sum property of a quadrilateral).

Now, focus on the third point of the above listed properties! The sum all the angles of a trapezium equals 360°. So, as per it, we shall be finding the value of the variable, by solving the equation:

$\: \: \: \underline{ \boxed{ \sf{ \pmb{ \angle A + \angle B + \angle C + \angle D = 360}}}}$

Let's solve it!

Solution:-

On substituting the values, we get,

$\\ \longmapsto{ \sf{z + (z + 7) + (2z + 39) + (3z + 6) = 360}}$

Now, grouping the like terms in the LHS results in,

$\\ \longmapsto{ \sf{z + z + 2z + 3z + 7 + 39 + 6 = 360}}$

Simplifying the LHS,

$\\ \longmapsto{ \sf{2z + 5z + 46 + 6 = 360}} \\ \\ \longmapsto{ \sf{7z + 52 = 360}}$

Transposing the like term from LHS to RHS (plus sign changes to minus sign),

$\\ \longmapsto{ \sf{7z = 360 - 52}}$

Simplifying the RHS,

$\\ \longmapsto{ \sf{7z = 308}}$

Again transposing the like term from LHS to RHS (multiplication sign changes to division sign),

$\\ \longmapsto{ \sf{z = 308 \div 7}}$

Finally, solving the RHS results as,

$\\ \longmapsto{ \sf{z = \dfrac{ \cancel{308}}{ \cancel{7}} }} \\ \\ \longmapsto \underline{\boxed{ \tt{ \red{ \pmb{z = 44}}}}}$

$\\ \therefore \underline{ \sf{ \pmb{The \: value \: of \: '\orange{z}' \: \: is \: \: \orange{44}.}}}$

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Answer 2

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎As per the analysis, we need to find the number of tiles required to pave the floor of the hall. How can we find it? We can find it using the topic - "Area of a rectangle and area of a square".

To find the required answer, we've to first find the area of the floor and the area of a tile. And then, we have to divide the area of floor by area of a tile, which is the required answer.

Before finding the areas, check whether the units of the measures of both the figures are same! Here, it isn't same. So, we have to convert the units from "metres" to "centimetres".

As we know, $\boxed{ \sf{1 \: m = 100 \: cm}}$,

$\\ \longmapsto{ \sf{25 \: m \: (length) = 25 \times 100 = 2500 \: cm}} \\ \\ \longmapsto{ \sf{18 \: m \: (breadth) = 18 \times 100 = 1800 \: cm}}$

Now, let's find the area of the floor –

$\longmapsto{ \sf{ \pmb{Area \: _{(rectangle)} = lb \: sq.units}}} \\ \\ \sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2500 \times 1800} \\ \\ \sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \underline{4500000 \: {cm}^{2}} }$

Finding the area of a tile –

$\longmapsto{ \sf{ \pmb{Area \: _{(square)} = {(s)}^{2} \: sq.units}}} \\ \\ \sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {(25)}^{2} } \\ \\ \sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \underline{625 \: {cm}^{2}} }$

Finally, let's find the number of tiles required by substituting the obtained measures in:

$\longmapsto{ \sf{ \dfrac{Area \: of \: floor \: of \: the \: hall}{Area \: of \: a \: tile} }} \\ \\ \longmapsto{ \sf{ \dfrac{ \cancel{4500000}}{ \cancel{625}}}} \\ \\ \longmapsto \underline{\boxed{ \tt{ \pmb{ \red{7200}}}}}$

$\\ \therefore \underline{ \sf{ \pmb{ \red{7200 \: tiles} \: are \: required \: to \: pave \: the \: floor .}}}$

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